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I have a tuff torq k57r hydrostatic transmission. Pedal control. How can I increase the speed of the transmission,or travel distance of the forward reverse lever ?

Post model & serial #'s of tractor, manufacturer John Deere, Cub Cadet, etc. how many hours on tractor? Have you removed deck & inspected drive belt & idler pulleys for replacement?

These only go so fast and are usually are already maxed control wise. If you are having slower than normal speeds then the unit needs rebuilding.

From Tuff Torq>

Loss of Power






If your transmission is having loss of power or no drive when it reaches operating temperature, it is likely that the cylinder blocks and center case need to be replaced. When replacing any of these components, it is critical to replace all components to include 2 cylinder block assemblies with new pistons and springs, and the center case.
If either the cylinder blocks or the center case has damage due to wear, then the associated parts will also have some degree of damage. If all are not replaced with new parts at the same time, it is very likely that you will have another failure within a short time.
There are many misguided blogs on the internet that say you can save money by not replacing all components. While this will likely work initially, it will result in a much earlier repeat failure than if you had replaced all recommended components. At this point, you cannot simply replace the components which you avoided in the first repair, as they will be damaged and you will still have to replace them to properly repair your unit.
We offer a complete repair kit that includes the center case, cylinder block assemblies and all gaskets, filters and sealant required to complete the repair.

End of Tuff Torq quoted info.

Also you need the serial number of the transaxle as there were three different K57R used,

Not really sure what you are asking
If the foot control moved the control lever on the transmission as far as it goes in both direction then there is no point in modifing it .
Transmission has a maximum input speed
You can fit a bigger engine pulley or smaller transmission pulley but check the maximum speeds , over speding the pulley will cause a big power drop and drastically shorten the service life of the pump/motor units $$$$$
Easiest thing is to fit bigger wheels but that will change the pitch angle of the deck plus reduce the load carrying capacity .